Problem: A big football championship will occur soon! n teams will compete in it, and each pair of teams will play exactly one game against each other.

There are two possible outcomes of a game:

  * the game may result in a tie, then both teams get 1 point; 
  * one team might win in a game, then the winning team gets 3 points and the losing team gets 0 points. 



The score of a team is the number of points it gained during all games that it played.

You are interested in a hypothetical situation when all teams get the same score at the end of the championship. A simple example of that situation is when all games result in ties, but you want to minimize the number of ties as well.

Your task is to describe a situation (choose the result of each game) so that all teams get the same score, and the number of ties is the minimum possible.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

Then the test cases follow. Each test case is described by one line containing one integer n (2 ≤ n ≤ 100) — the number of teams.

Output

For each test case, print (n(n - 1))/(2) integers describing the results of the games in the following order: the first integer should correspond to the match between team 1 and team 2, the second — between team 1 and team 3, then 1 and 4, ..., 1 and n, 2 and 3, 2 and 4, ..., 2 and n, and so on, until the game between the team n - 1 and the team n.

The integer corresponding to the game between the team x and the team y should be 1 if x wins, -1 if y wins, or 0 if the game results in a tie.

All teams should get the same score, and the number of ties should be the minimum possible. If there are multiple optimal answers, print any of them. It can be shown that there always exists a way to make all teams have the same score.

Example

Input


2
2
3


Output


0 
1 -1 1 

Note

In the first test case of the example, both teams get 1 point since the game between them is a tie.

In the second test case of the example, team 1 defeats team 2 (team 1 gets 3 points), team 1 loses to team 3 (team 3 gets 3 points), and team 2 wins against team 3 (team 2 gets 3 points).

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {
    static PrintWriter pw;
    static Scanner sc;
    static long ceildiv(long x, long y) { return (x+y-1)/y; }
    static int mod(long x, int m) { return (int)((x%m+m)%m); }
    static void put(HashMap<Integer, Integer> map, Integer p){if(map.containsKey(p)) map.replace(p, map.get(p)+1); else map.put(p, 1); }
    static void rem(HashMap<Integer, Integer> map, Integer p){ if(map.get(p)==1) map.remove(p);else map.replace(p, map.get(p)-1); }
    static void printf(double x, int dig){ String s="%."+dig+"f"; pw.printf(s, x); }
    static int Int(boolean x){ return x?1:0; }
    static final int inf=(int)1e9, mod=998244353;
    static final long infL=inf*1l*inf;
    static final double eps=1e-9;
    public static long gcd(long x, long y) { return y==0? x: gcd(y, x%y); }
    public static void main(String[] args) throws Exception{
        sc=new Scanner(System.in);
        pw=new PrintWriter(System.out);
        int t=sc.nextInt();
        while(t-->0)
            testcase();
        pw.close();
    }
    static void testcase() throws IOException{
        int n=sc.nextInt(), max=((n-1-((n-1)%2))/2)*3+(n-1)%2;
        int[] score=new int[n];
        TreeMap<Integer, TreeSet<Integer>> map=new TreeMap<>();
        map.put(0, new TreeSet<>());
        TreeSet<Integer> draw=new TreeSet<>();
        for (int i = 0; i < n; i++){
            map.get(0).add(i);
            if(n%2==0)
                draw.add(i);
        }
        for (int i = 0; i < n; i++) {
            int curr=score[i], need=max-curr, win=need/3, tie=need%3, lose=n-1-i-win-tie;
            map.get(curr).pollFirst();
            if(map.get(curr).isEmpty())
                map.remove(curr);
            TreeMap<Integer, Integer> ans=new TreeMap<>();
            if(draw.contains(i))
                draw.remove(i);
            while(tie-->0){
                int x=draw.first();
                map.get(score[x]).remove(x);
                if(map.get(score[x]).isEmpty())
                    map.pollFirstEntry();
                score[x]++;
                if(!map.containsKey(score[x]))
                    map.put(score[x], new TreeSet<>());
                map.get(score[x]).add(x);
                ans.put(x, 0);
            }
            while(lose-->0){
                int x=map.get(map.firstKey()).pollFirst();
                if(map.get(score[x]).isEmpty())
                    map.pollFirstEntry();
                score[x]+=3;
                if(!map.containsKey(score[x]))
                    map.put(score[x], new TreeSet<>());
                map.get(score[x]).add(x);
                ans.put(x, -1);
            }
            for (int j = i+1; j < n; j++)
                pw.print((ans.containsKey(j) ? ans.get(j) : 1) + " ");
        }
        pw.println();
    }
    static void printArr(int[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i] + " ");
        pw.println();
    }
    static void printArr(long[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i] + " ");
        pw.println();
    }
    static void printArr(double[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i] + " ");
        pw.println();
    }
    static void printArr(Integer[] arr) {
        for (int i = 0; i < arr.length; i++)
            pw.print(arr[i] + " ");
        pw.println();
    }
    static void printArr(ArrayList list) {
        for (int i = 0; i < list.size(); i++)
            pw.print(list.get(i)+" ");
        pw.println();
    }
    static void printArr(boolean[] arr) {
        StringBuilder sb=new StringBuilder();
        for(boolean b: arr)
            sb.append(Int(b));
        pw.println(sb);
    }
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;
        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
        public int[] nextDigits() throws IOException{
            String s=nextLine();
            int[] arr=new int[s.length()];
            for(int i=0; i<arr.length; i++)
                arr[i]=s.charAt(i)-'0';
            return arr;
        }
        public int[] nextArr(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < arr.length; i++)
                arr[i] = nextInt();
            return arr;
        }
        public Integer[] nextsort(int n) throws IOException{
            Integer[] arr=new Integer[n];
            for(int i=0; i<n; i++)
                arr[i]=nextInt();
            return arr;
        }
        public Pair nextPair() throws IOException{
            return new Pair(nextInt(), nextInt());
        }
        public long[] nextLongArr(int n) throws IOException{
            long[] arr=new long[n];
            for (int i = 0; i < n; i++)
                arr[i]=sc.nextLong();
            return arr;
        }
        public Pair[] nextPairArr(int n) throws IOException{
            Pair[] arr=new Pair[n];
            for(int i=0; i<n; i++)
                arr[i]=nextPair();
            return arr;
        }
        public boolean ready() throws IOException {
            return br.ready();
        }
    }
    static class Pair implements Comparable<Pair>{
        int x;
        int y;
        public Pair(int x, int y) {
            this.x=x;
            this.y=y;
        }
        public boolean contains(int a){
            return x==a || y==a;
        }
        public int hashCode() {
            return (this.x*1000000000+this.y);
        }
        public int compareTo(Pair p){
            if(x==p.x)
                return y-p.y;
            return x-p.x;
        }
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (this.getClass() != obj.getClass()) {
                return false;
            }
            Pair p = (Pair) obj;
            return this.x==p.x && this.y==p.y;
        }
        public Pair clone(){
            return new Pair(x, y);
        }
        public String toString(){
            return this.x+" "+this.y;
        }
        public void add(Pair p){
            x+=p.x;
            y+=p.y;
        }
        public Pair negative(){
            return new Pair(-x, -y);
        }
    }
    static class LP implements Comparable<LP>{
        long x, y;
        public LP(long a, long b){
            x=a;
            y=b;
        }
        public void add(LP p){
            x+=p.x;
            y+=p.y;
        }
        public boolean equals(LP p){
            return p.x==x && y==p.y;
        }
        public String toString(){
            return this.x+" "+this.y;
        }
        public int compareTo(LP p){
            int a=Long.compare(x, p.x);
            if(a!=0)
                return a;
            return Long.compare(y, p.y);
        }
    }
    static class Triple implements Comparable<Triple>{
        int x, y, z;
        public Triple(int a, int b, int c){
            x=a;
            y=b;
            z=c;
        }
        public int compareTo(Triple t){
            if(this.y!=t.y)
                return y-t.y;
            return x-t.x;
        }
        public String toString(){
            return x+" "+y+" "+z;
        }
    }
    //    static class MaxSegmentTree{
//        int n;
//        long[] tree;
//        public MaxSegmentTree(int len, long[] arr){
//            n=len;
//            build(0, 0, n-1, arr);
//        }
//        public void build(int i, int l, int r, long[] arr){
//            if(l==r){
//                tree[i]=arr[l];
//                return;
//            }
//            int mid=(l+r)/2, left=2*i+1, right=2*i+2;
//            build(left, l, mid, arr);
//            build(right, mid+1, r, arr);
//            tree[i]=Math.max(left, right);
//        }
//        public int query(int i){
//            return query(0, 0, n-1, 0, i);
//        }
//        public int query(int node, int i, int j, int l, int r){
//            if(l>j || r<i)
//                return -1;
//
//        }
//    }
    static class SegmentTree {
        int n, size[];
        long[] tree;
        public SegmentTree(int len) {
            n = len;
            tree=new long[2*n-1];
            size=new int[2*n-1];
        }
        public void set(int i, long x){
            i+=n-1;
            tree[i]=x;
            size[i]++;
            i=(i-1)/2;
            while(true){
                size[i]++;
                tree[i]=tree[i*2+1] + tree[i*2+2];
                if(i==0)
                    break;
                i=(i-1)/2;
            }
        }
        public long query(int x){
            return query(0, 0, n-1, x+1, n-1);
        }
        public long query(int node, int i, int j, int l, int r){
            if(j<l || i>r)
                return 0;
            if(i>=l && j<=r)
                return tree[node];
            int mid=(i+j)/2, left=node*2+1, right=node*2+2;
            return query(left, i, mid, l, r) + query(right, mid+1, j, l, r);
        }
        public int size(int idx){
            return size(0, 0, n-1, idx+1, n-1);
        }
        public int size(int node, int i, int j, int l, int r){
            if(i>r || j<l)
                return 0;
            if(i>=l && j<=r)
                return size[node];
            int mid=(i+j)/2, left=node*2+1, right=node*2+2;
            return size(left, i, mid, l, r)+size(right, mid+1, j, l, r);
        }
    }
}